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Lock Free Contention Adaptive Trees

Intro

The following article contains excerpts from a research paper submitted as part of a group project in advanced concurrent data structures. The main purpose of this project was to analyze and implement a previously published research paper of our choosing relating to modern solutions for concurrency problems in multi-core processing. We chose to implement Lock-Free Contention Adaptive Trees (LFCAT) originally published by Uppsala University. As one of the main leads on the project I was responsible for putting together much of the code and analysis presented in the final report.

The Problem

As the prevalence of digital technology in modern society has steadily increased over the past decade, so too has the quantity of information that has been produced. The efficient acquisition, processing, and utilization of these massive unstructured data sets has become a crucial area of research. Cloud processing of this “Big Data” has become incredibly common as different industries rely on insights from analyzing this data to make long-term business decisions in real-time. Unfortunately, traditional relational database models have trouble adapting to the variety and scale of such large sets of data as they require a fixed predefined structure, complex fail-over schemes, and costly partitioning to handle the increased capacity. Alternatively, modern NoSQL databases attempt to provide scalability, performance, availability, and flexibility as a means of coping with variety, throughput, and amount of data with which modern database systems must handle.

One innovative implementation of a NoSQL database is known as the key-value store model. This model is quite flexible as it simplifies the storage problem to a key used for indexing within the structure, and a value or a set of values to be stored as a generic blob. This simplicity means that it is easy to perform single-item operations including contains, insert, and remove as well as multi-item operations including range query which returns all values whose keys are within a specified range. However, the problem of data contention, that is multiple operations seeking to utilize the same data, is still a limiting factor for the performance of the database especially as the number of cores in a system increases.

Solving The Problem Through Adaptation

To better understand the problem of contention in the key-value model, consider a binary tree holding a set of keys in the leaf nodes. When a static synchronization strategy with a fixed granularity is used to overcome contention within the tree, either single-key operations such as insert, remove, and contains will perform well or multi-key operations such as range query will, but not both. If a fine-grain synchronization strategy is used, single-key operations will perform well since they will experience contention infrequently, but multi-key operation performance will suffer since the operations must perform a large amount of overhead to access each node in the query. Conversely, if a coarse-grain synchronization strategy is used, multi-key operations will perform well since fewer places in the tree require synchronization, but single-key operations will perform worse since more contention will occur even if the single-key operations are being performed on different nodes that are logically unrelated. Attempting to fine-tune the granularity of synchronization cannot account for both cases efficiently. To do so would require a priori knowledge of the level of contention and the distribution of the operations to be performed. Worse, if the amount of contention within the tree changes over time or different parts of the tree experience differing amounts of contention, static approaches cannot account for these types of variations.

A dynamic synchronization strategy that adapts to the amount of contention that is occurring within a part of the tree at a given time can outperform static synchronization strategies. Leaf nodes that experience a high amount of contention from many single-key operations colliding at a node are split into multiple nodes with a new route node connecting the two together to reduce contention. Leaf nodes that experience low amounts of contention from use predominately with multi-key operations and few single-key operations are merged with neighboring nodes to reduce synchronization overhead when multi-key operations operations are performed.

LFCAT Structure

The LFCAT data structure is defined by a number of specialized nodes: route nodes, base nodes, join-main nodes, join-neighbor nodes, and range nodes. Each node has its own purpose and descriptive state that collectively describe the full state of the LFCAT. Route nodes are used to define the path from the root node to a given leaf node. Like a standard binary search tree, the route nodes each contain a key that is used to properly order the tree. Key indexes are used to traverse route nodes until a leaf node is found. The leaf nodes are defined as base nodes, and they contain the actual dataset stored as sets of key-value pairs. The three remaining node types are used to implement the split, join, and range query methods which are described below.

The structure of the dataset held in each base node is not constrained to be of any particular type. Because the storage mechanism is independent of the LFCAT protocols, the datasets can be any container that holds the key-value pairs. While the datasets are not the main focus of this paper, we should note that Sagonas, Winblad, and Jonsson used a simple treap structure in their paper largely due to their efficiency in distributing values thus providing O(log n) lookup times. We sought to preserve the order of the keys in each dataset, and opted to use an AVL tree in our implementation because AVL trees are guaranteed to be balanced whereas treaps are randomly ordered.

Contention Adaptations

Updates to any node in the LFCAT require that a local node be created, then modified, and swapped with the original node using a Compare-And-Swap (CAS) operation. The CAS is the linearization point of each operation as it is the moment when the local modification become visible in the LFCAT. A failed CAS operation indicates that the original node is experiencing contention. If the original node is a base node, its heuristic value is increased and the update is attempted again. Repeated failures of single-key operations, like insert and remove, will drive up the contention heuristic, indicating that the target node contains a frequently accessed set of keys and that the base node should be split in order to reduce the contention.

Split Contention

When a base node is split, each half of the original AVL tree is assigned to its own local base node. A local route node is created containing the split key of the original AVL tree, and the local base nodes are set as the route node’s children. The update to the LFCAT structure takes effect when the old base node is swapped with the new route node using CAS. This process is shown in the figure above. By splitting the base node, the contention on this set of keys is lowered, prompting fewer CAS failures, thus increasing the performance of the LFCAT for single-key operations.

High Contention Adaptation

Another common operation required of key-value store models is the range query, which returns as set of key-value pairs within a specified key range. Range queries are difficult to optimize because the number of key-value pairs that will be returned is not known in advance. Given a search range, the range query operation traverses the structure, saving the nodes encountered in stacks, and marking the relevant nodes. The figure above shows an example of a range query traversal. The operation begins by traversing the LFCAT to find the base node containing the lowest key within the specified range. The base node and its parent are then placed in a stack. These nodes are marked as being a part of the range query by replacing their nodes with range node copies via CAS. Starting from the base node with the lowest key in the range, the range query operation checks the next leftmost node that has yet to be visited. This is repeated until a base node containing a key that matches or exceeds the upper limit of the range is reached. The stack of verified nodes is then traversed in order to join each AVL tree into one result set. Other threads see a range query is complete when the result set is populated. This is the linearization point of the range query.

Low Contention Adaptation

Unlike the individual node access of the insert and remove operations, range query performance is adversely affected by sparsely distributed keys. Collecting keys spread over multiple nodes requires more work for the range query operation because each node within the range of the query must be replaced with a range node using CAS. The more nodes a range query contains, the more nodes that must be swapped thereby increasing the overhead. When a query encounters a range that contains multiple base nodes, the contention heuristic for those nodes is lowered. Like the single-key operations, the range query also compares each node’s heuristic to the contention thresholds and adapts if needed. If there are fewer CAS failures than there are multi-node ranges, the contention heuristic will eventually drop low enough to call for the joining of one or more base nodes. By performing this adaptation, future range queries will not have to swap as many nodes, thereby increasing the throughput. Performance of single-key operations can also be improved if little or no contention is experienced by making the path to a node shorter.

For low contention adaptation, two base nodes are merged via the join operation, resulting in a coarser granularity for the key distribution. When a join operation is performed on a base node, the process is split into two parts labeled as secure join and complete join. Secure join, as diagrammed in the figure above, starts by swapping the base node with a join-main node using CAS. Next, the leftmost neighbor (i.e. the next base node in key order) is found via a depth-first traversal and swapped with a join-neighbor node, again using CAS. These two join nodes indicate to other threads that a join operation is in progress and that these nodes may not be replaced until the join is complete or aborted.

If these CAS operations are successful then the algorithm must also notify the grandparent route node of the target, since it will point to the newly joined base node once the join operation is complete. This notification takes place through the CAS of an atomic reference variable in the grandparent node, with the newly created join-main node. This CAS can only succeed if no other node has marked the grandparent node for a join operation. Once the grandparent is successfully notified, another CAS operation takes place where one of the join-main node’s atomic references is swapped to point to a new base node that stores the combined AVL tree of the join-main and join-neighbor nodes. Up to this point any other operation could intercede and mark the join-main node as ‘aborted’ since any operation has higher priority than node maintenance.

Once the join-main node’s reference has been changed from a static ’preparation’ node to a local joined node, the join operation is ready to be finalized via complete join as shown in the figure above. From this point on, other operations will attempt to help complete the join operation rather than simply aborting it. To complete the join operation the parent route of the target node is logically marked as invalid, and any existing grandparent is made to point to the replacing structure. If the join-neighbor node was a direct sibling of the join-main node, then the replacement of the parent route node is simply the newly created base node containing the joined data. However, if the join-neighbor node is the result of a deeper sub-node structure then the parent node will be replaced by the top Route node that leads to that join-neighbor node from the targets parent. The join-main node is no longer a logical part of the LFCAT structure, but to describe it’s logical removal to other operations the join must logically mark the node as completed by atomically setting one of it’s references to a static ’done’ node.

Implementation Details

Our implementation follows along with the basic concepts of the LFCAT structure as described in the original paper. However, unlike the C based pseudo-code provided by the authors, our implementation attempts to provide an object-oriented alternative written in Java. Using polymorphic objects that implement generic interfaces allows us the flexibility to create a more dynamic storage structure than that of the provided pseudo-code. Java was selected as the implementation language largely due to it’s abstracted object reference model and automated garbage collection. By removing the need for manual memory management techniques, like object pooling, we simplify the overall structure and can better focus on the algorithm implementation. Of course, this simplification will likely result in lower performance as we do not have complete control over how, or when, memory gets collected nor can our algorithm recycle memory locations that have already been allocated.

The most basic building block of our LFCAT structure is a Node class with abstract methods that all other node types must implement. The Node class keeps track of the current parent and usage statistics as well as ensuring that all other nodes can report whether they are: in a replaceable state, in need of adaptation, or in need of assistance. The actual implementation of these functions is left to the node types as each type has different behaviors under different conditions. Base nodes inherit from node, but also contain an AVL tree member variable where in the actual key-value pairs will be stored. This type of object oriented paradigm is used across our structure to provide a separation of concerns over the different node types that leads to increased legibility, ease of use, and possible extensions in future work.

Our implementation also differs from the original LFCAT structure in that we have introduced the size of the AVL tree as a consideration in the statistics used for node adaptation. Our implementation requires any update operation to make a full copy of the AVL tree in a given node before attempting a CAS with the new local node. This copy is expensive as it increases linearly with the number of nodes in the AVL tree. As the leaf node gets larger, this cost becomes prohibitively expensive as most of the time of an update is spent on copying the AVL tree before being updated. This cost is specially apparent when update operations fail, as they will need to recopy the AVL tree from the new node in order to attempt their update again. By introducing the tree size as a factor in the node statistic we are forcing a balanced LFCAT structure that still allows for contention adaptations while distributing the load across nodes.

In the early stages of our implementation we found that update operations from multiple threads at one time could easily conflict and enter a race condition cycle of continuously attempting the same operations. The original LFCAT implementation should address this through the high contention adaption and by allowing threads that fail the update the chance to help other threads with ongoing operations. Allowing the failed threads to provide continuing progress as well as a pseudo back-off so that failed threads do not all reattempt at the same time. However, we found that under a high amount of contention the update operations would often not be able to complete the split adaptation before another thread invalidated the split node. Also, update operations cannot assist each other, which means that if multiple threads with updates fail because of another update operation they will all reattempt their updates at the same time. To help alleviate this contention we introduced an elimination back-off to our update operations in the LFCAT structure. If an operation fails and cannot assist another node then it must wait for a small period of randomly selected time before attempting the operation again. If the operation continues to fail the guaranteed amount of wait time is exponentially increased.

Conclusion

This article presents an overview of the Lock-Free Contention Adaptive Search Tree along with an implementation in Java. The code is accessible at the repository linked in the abstract. The performance of our implementation was tested under varying operational loads and levels of concurrency. Our implementation comes close to the performance reported in the original paper. The differences can be attributed to the use of Java instead of C. Our implementation sacrifices the better performance for automatic memory management which simplified implementation. Overall, the LFCAT presents an efficient algorithm that performs well under both low-contention and high-contention conditions and can scale efficiently with additional processors. By adapting the structure of the tree to the local spatial and temporal contention, the LFCAT performs on par with comparable algorithms designed for specific scenarios and can significantly outperform those same algorithms for scenarios that are not optimized for. The LFCAT is an efficient solution to bridge the gap between fine-grain and course-grain synchronization approaches.